Use the Pythagorean theorem:
[tex]a^2+(2\sqrt3)^2=(4\sqrt3)^2\\\\a^2+2^2(\sqrt3)^2=4^2(\sqrt3)^2\\\\a^2+4\cdot3=16\cdot3\\\\a^2+12=48\ \ \ \ |-12\\\\a^2=36\to a=\sqrt{36}\\\\\boxed{a=6\to C.}[/tex]
Used:
[tex](a\cdot b)^n=a^n\cdot b^n\\\\(\sqrt{a})^2=a[/tex]
